As with knives good stones can get real expensive real quick. I use single grit stones from 100, 500, 800, 1000, 2000, 3000, 5000, 8000, 10000
On touch up I skip all stones under 2000. Sharpening takes a while this way and only a true sharpening snob will notice the difference. For everyone else:
I would say get a dual grit stone (water) of 1000 / 3000. The trick with a stone like this is to keep touching up regularly. If you let the blade go truly dull or damage it you are going to need a coarser stone to bring it back.
Japanese waterstone is your search term.
The cheaper stones don't necessarily sharpen worse but are much softer and wear quicker. So replace more often. I buy the for axes and chisels and they last me a couple of years. Cheaper stones tend to be a smaller too. Larger is easier.
If I had to advise just one stone it would be this one:
https://www.amazon.it/gp/aw/s/ref=i...010-9798809?k=naniwa+1000+3000&sprefix=naniwa
It's the same brand as my single grit stones and excellent but more intended for the average user that wants a sharp knife. It's a large hard synthetic stone which means the wear is low and it doesn't need to soak in water an hour before use. Simply wet and go.
As to price this is probably the at the cheaper end of the really good stones but still expensive.
It's just like tools, some are happy with craftsmen and some want snap on and some want PB Swiss. Naniwa stones are wiha going on PB Swiss. The one I linked is entry level but will get your knife shaving sharp everytime.
I also chose this one because it lasts and I like tools that last.
I could write an essay on waterstone sharpening. If you need more advice feel free to pm me.
This is a cheaper alternative that would work fine too but smaller and will wear faster:
https://www.amazon.it/gp/aw/d/B00YM...X236_SY340_QL65&keywords=waterstone+1000+3000
Note: this cheaper type stone needs about half and hour to an hour soak in water before use.
Finally just like old fashioned razor blades always strop your knife after sharpening on a piece of leather with some fine grit polishing compound (5000 or finer) on it. This finishing touch makes all the difference.
Edit:
Had to wait till I was home to do a pic of a cheap stone vs naniwa. Same age (2 years) roughly same and similar use:
The grits are not quite the same but close enough.
The naniwa in the background is the 1000 / 3000 linked above
When a stone wears hollow like that it becomes less good for a flat grind but excellent for a convex like on an axe or cleaver
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